Anywhere inside the USA where AT&T has native coverage, your plan is effective without any roaming surcharge.
There's a small caveat to that statement:
If you're moving around within an area where you are switching back and forth between AT&T's native infrastructure, and a domestic 3rd party partner carrier, then there are soft caps on what maximum percentage of your plan allotment of voice minutes, text messages, and data may be spent on the 3rd party network.
If you stay within those soft caps, then your regular rates apply and you won't know the difference between operating on AT&T's native network versus the domestic 3rd party carrier. However, if you exceed those soft caps, then you might end up getting switched to a plan which charges extra when you're operating on the 3rd party carrier's network, or else getting switched to a plan that doesn't let you use the 3rd party carrier at all. Neither of those corrective actions will be taken without alerting you of the problem first to give you a chance to adjust your behaviour voluntarily first.
This could happen anywhere within the USA, not just in Texas. But since you'll be travelling, it is possible that you aren't familiar yet with which parts of Texas are covered by AT&T natively, and which parts are covered by a 3rd party partner.